# Modular Inverses

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This is a visual map of multiplicative inverses modulo . The integers from to are placed clockwise on a circular number line with at the top. Two integers that are inverses modulo are connected by an arrow. An integer that is its own inverse is marked by a colored dot. Those integers that have no inverse modulo are not marked.

Contributed by: Aaron Dunigan AtLee (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: for , all integers that have inverses are inverses of themselves

Snapshot 2: for some values of , the inverse map demonstrates four-fold rotational symmetry

Snapshot 3: for prime , all integers have inverses, so the map is much more detailed

## Permanent Citation